Enhanced Fault-Tolerant Quantum Computing in d-Level Systems

Error-correcting codes protect quantum information and form the basis of fault-tolerant quantum computing. Leading proposals for fault-tolerant quantum computation require codes with an exceedingly rare property, a transversal non-Clifford gate. Codes with the desired property are presented for d-level qudit systems with prime d. The codes use n = d - 1 qudits and can detect up to similar to d/3 errors. We quantify the performance of these codes for one approach to quantum computation known as magic-state distillation. Unlike prior work, we find performance is always enhanced by increasing d.